[seqfan] Re: Square forest

[Rémy Etc]

hi John,

> I was surprised not to see this sequence in the database; maybe someone will recognise the idea and point to something similar.
here are two similar sequences:
A049691     a(n)=T(n,n), array T as in A049687. Also a(n)=T(2n,2n),
array T given by A049639.
A137243     Number of coprime pairs (a,b) with -n <= a,b <= n.

best regards,

Rémy

Le sam. 22 mai 2021 à 17:45, John Mason <masonmilan33 at gmail.com> a écrit :
>
> Hi Seqfans,
> I was surprised not to see this sequence in the database; maybe someone will recognise the idea and point to something similar.
>
> A forest of trees has been planted on a square grid pattern, n rows by n columns. Each row is separated from the next by one metre, and the same for the columns.
> An observer stands in the middle of one side, exactly one metre outside the forest.
> How many trees trunks can the observe see? Assume that the trunks are very thin, and that any trunk obscures the vision only of other trunks that are perfectly behind it, from the point of view of the observer.
>
> I calculated the following values: 1, 4, 7, 14, 17, 30, 33, 52, 51, 82, 81, 108, 105, 156, 143, 198, 183, 252, 231, 308, 267, 380, 339, 436, 383, 526, 461, 598, 525, 680.
> For example, if the forest contains 5 by 5 trees, the observer will see only 17, as 8 will be hidden.
> The sequence does not seem to be present, and neither is its “opposite”, the number of hidden trees: 0, 0, 2, 2, 8, 6, 16, 12, 30, 18, 40, 36, 64, 40.
> I tried searching alternate values too, but to no avail.
> I don’t know if there is a formula that will predict a(n); I used simple geometry to find the hidden trees.
>
> john
>
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